If you come to my house for dinner, you will almost certainly be served these rolls if you're not served my famous breadsticks. So, to start out with, the original recipe, again from the King Arthur Flour people, is called "Moomie's Beautiful Burger Buns," and is made with all-purpose flour instead of whole wheat and includes an egg, which I don't use because I think the texture of the rolls isn't as good. It also calls for butter, and, interestingly enough, I find that vegetable oil gives a better result. You can certainly use butter if you like. And . . . I use honey instead of sugar, but not because honey is any better for you than sugar. I just like the taste.
*You have three choices for flour here:
1) All-purpose flour
2) Whole-wheat flour bought from the grocery store, but be sure to check the expiration date and keep the flour in your freezer. The reason why people think they don't like whole-wheat flour is that it's often rancid. Since the perishable germ of the wheat kernel is retained, the shelf life of whole wheat flour is much shorter than that of white.
3) Freshly-ground flour from your grain mill. I find that I get double the volume of flour from the wheat, but I've read other sources that say more like 1 1/2 times the volume, so you would need to measure what you get with your wheat and your mill for the first few times. Once you've figured it out, then you don't need to measure the resulting flour. Get the mill going while you measure the rest of the ingredients.
**Easiest way to do this is to use a two-cup Pyrex measuring cup, putting water and honey in first to their respective lines and then sort of guessing where the 1/3 cup of oil goes--it will be a little above the 1 1/2-cup line, say about 1/3 of the way to the 1 3/4-cup line. Exact measurements aren't necessary. Then nuke the whole thing for a minute, stir well, and pour into the bread machine.
***In the past I have used SAF Red Instant yeast from King Arthur Flour, but their shipping charges have gotten kind of outrageous. They used to base their charges on the actual weight of the item but then changed over to the dollar amount; the shipping on one $5.95 16-oz. bag of this yeast is $6.00. Of course I'd never do it that way; I'd always buy other things, too, but now I see that if I buy two packages of this yeast my shipping goes up to $8.00. Sorry, pals! That ain't gonna happen. Honeyville has it for $10.99 per pound, so I'm still paying about the same with them even with their much lower shipping charges. So, once I used up the SAF yeast I had, I bought some plain old Red Star yeast at Costco, and I think I like it even better. If you do a lot of yeast baking you absolutely don't want to buy those little packets of yeast at the grocery story, as it's very expensive to buy yeast that way. You can at least buy a jar of yeast there if you don't belong to Costco. (But why don't you?) Keep the bag or jar in your freezer.